Image generation using subscaling and depth up-scaling

ABSTRACT

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for generating output images. One of the methods includes obtaining data specifying (i) a partitioning of the H by W pixel grid of the output image into K disjoint, interleaved sub-images and (ii) an ordering of the sub-images; and generating intensity values sub-image by sub-image, comprising: for each particular color channel for each particular pixel in each particular sub-image, generating, using a generative neural network, the intensity value for the particular color channel conditioned on intensity values for (i) any pixels that are in sub-images that are before the particular sub-image in the ordering, (ii) any pixels within the particular sub-image that are before the particular pixel in a raster-scan order over the output image, and (iii) the particular pixel for any color channels that are before the particular color channel in a color channel order.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Application No.62/737,814, filed on Sep. 27, 2018. The disclosure of the priorapplication is considered part of and is incorporated by reference inthe disclosure of this application.

BACKGROUND

This specification relates to generating images using neural networks.

Neural networks are machine learning models that employ one or morelayers of nonlinear units to predict an output for a received input.Some neural networks include one or more hidden layers in addition to anoutput layer. The output of each hidden layer is used as input to thenext layer in the network, i.e., the next hidden layer or the outputlayer. Each layer of the network generates an output from a receivedinput in accordance with current values of a respective set ofparameters.

SUMMARY

This specification describes a system implemented as computer programson one or more computers in one or more locations that generates animage using a generative neural network.

In some implementations, the system implements subscaling. Inparticular, the system generates an H×W×C×D output image (where H and Ware respectively the height and width of the image in numbers of pixels;C is the number of channels, e.g. 3, and D is the number of bits in eachchannel) by partitioning the H by W pixel grid of the output image intoK disjoint, interleaved sub-images, where K is an integer that is lessH. The sub-images are referred to as interleaved because pixels withinone sub-image are generally separated from other pixels within the samesub-image by pixels in another sub-image. For example, if there are 4sub-images, every 4^(th) pixel along the horizontal dimension will be inthe same sub-image and every 4^(th) pixel along the vertical dimensionwill be in the same sub-image. The system then generates the outputimage sub-image by sub-image using a generative neural network, i.e.,following an ordering of the sub-images, e.g., a raster-scan ordering.

In some implementations, the system implements depth upscaling (e.g. ofan image of the real world, e.g. captured by a camera) in addition to orinstead of subscaling. In particular, when generating an image thatincludes N bit intensity values, the system first generates an initialoutput image that has b bit intensity values (where b is less than N)and then generates the remaining N-b bits of each intensity valueconditioned on the initial output image. For the generation of eitherthe initial output image or the final output image or both, the systemcan implement subscaling.

Certain novel aspects of the subject matter of this specification areset forth in the claims below.

The subject matter described in this specification can be implemented inparticular embodiments so as to realize one or more of the followingadvantages.

Conventional autoregressive generative neural networks are generallyonly able to generate high fidelity images when the sizes of the imagesthat they are configured to generate are relatively small and even thenthese models tend to require a large amount of memory and computation togenerate the image. In particular, generating larger imagesautoregressively requires encoding a vast context when generating atleast some of the intensity values in the image and training thegenerative neural network requires learning a distribution over a verylarge number of variables that preserves both global semantic coherenceand exactness of detail. The described systems, on the other hand, cangenerate high fidelity images even when the sizes of the images arelarge while preserving image-wide spatial dependencies that areresponsible for the high quality of images generated by autoregressivegenerative neural networks. In particular, the described systemsgenerate an image as a sequence of sub-images. This allows the describedsystem to preserve in the sub-images the spatial structure of the pixelswhile compactly capturing image-wide spatial dependencies. Thus, thedescribed systems require only a fraction of the memory and thecomputation that would otherwise be required to generate a large imagewhile still generating high fidelity images. Additionally, the describedsystems can perform depth-upscaling, i.e., first generating a firstsubset of the bits of all of the intensity values in the image and thengenerating the remaining bits conditioned on the first subset, tofurther increase the capacity of the described systems for generatingvery high-fidelity large-scale image samples.

The reduction in memory and processing power requirement makes someimplementations of the present concepts suitable for use in mobiledevices, such as mobile devices including a unit (e.g. a camera) whichis used for capturing an image of the real world which is used (possiblyfollowing some pre-processing) in some implementations of the conceptsdescribed herein as an input image to the image generation system.

The details of one or more embodiments of the subject matter describedin this specification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates different techniques that can be employed by an imagegeneration system when generating an image.

FIG. 2 shows an example image generation system.

FIG. 3 shows another example image generation system.

FIG. 4 is a flow diagram of an example process for generating an outputimage using subscaling.

FIG. 5 is a flow diagram of an example process for generating an outputimage using depth upscaling.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

This specification describes an image generation system that generatesimages using a generative neural network.

As will be described below, in some implementations, the systemgenerates images unconditionally, i.e., generates images that appear asif they were images drawn from a training set used to train the imagegeneration system but that are not otherwise conditioned on any externalinput.

In some other implementations, the system generates higher-resolutionimages conditioned on a lower-resolution input image, i.e., the systemperforms super-resolution to generate higher-resolution versions ofinput images.

In some other implementations, instead of or in addition to increasingthe resolution of the input image, the system can increase the qualityof the input images by converting the intensity values in the inputimage to a higher bit depth, e.g., converting input images from 3 bitintensity values to 8 bit intensity values or converting input imagesfrom 6 bit intensity values to 16 bit intensity values. Generally, thesystem can convert input images from a low bit depth to a higher bitdepth, i.e., with the low bit depth being one half or less than one halfof the higher bit depth.

In some other implementations, the system receives a differentconditioning input (e.g. a conditioning input which is not itself animage, and may not have components that correspond to respectiveportions of the output image) that identifies properties of an image andgenerates an output image that has the identified properties.

FIG. 1 illustrates different techniques that can be employed by theimage generation system when generating an output image.

In the examples of FIG. 1, the output image being generated by thesystem is a 4×4 image that therefore includes 16 pixels for whichintensity values need to be generated to generate the output image. Togenerate an output image, the system generates, for each pixel,respective intensity values for each of one or more color channels. Whenthe image generation system is configured to generate greyscale images,there is only a single color channel per pixel. When the imagegeneration system is configured to generate color images, there aremultiple color channels per pixel. For example, the set of colorchannels can include a red color channel, a green color channel, and ablue color channel. As a different example, the set of color channelsinclude a cyan color channel, a magenta color channel, a yellow colorchannel, and a black color channel. When there are multiple colorchannels, the multiple color channels are arranged according to apredetermined channel order, e.g., red, green, and then blue, or blue,red, and then green.

FIG. 1 includes an illustration 102 of a generation order for aconventional technique for generating intensity values for an outputimage.

In the generation order shown in the illustration 102, the systemgenerates the intensity values for the 16 pixels in the image in araster-scan order. In raster-scan order, the system starts at the topleft (pixel #1) and then proceeding row by row along the image untilreaching the bottom right (pixel #16). Within each pixel, the systemgenerates the intensity values for the color channels according to thepredetermined channel order, e.g., first red, then green, then blue orfirst blue, then red, then green.

Generally, to improve the quality of the generated image, the systemwould generate the intensity values for each pixel autoregressively, sothat the intensity value for a given color channel for a given pixel isconditioned on the intensity values that have already been generated,i.e., on the intensity values for pixels that are ahead of (i.e. before)the given pixel in the generation order and any intensity values for thegiven pixel that have already been generated (when the given colorchannel is not the first color channel in the predetermined order).Thus, the intensity values for the bottom left pixel (pixel #11) wouldbe conditioned on the intensity values for pixels 1 through 10 in theordering. The system can generate these intensity values value by valueusing a generative neural network, i.e., by conditioning the generativeneural network differently for each value that needs to be generated.

However, when images become large, generating the intensity values inthis manner requires encoding a vast context when generating at leastsome of the intensity values in the image, e.g., pixels that are nearthe end of the generation order. That is, when the number of pixels inthe image becomes large, generating the intensity value for a pixel thatis near the end of the order requires conditioning the generative neuralnetwork on a very large number of intensity values, i.e., intensityvalues for almost all of the pixels in the very large image. This makesgenerating the output image very computationally intensive and trainingthe generative neural network to generate high quality images verydifficult and, in at least some cases, infeasible when the image size islarge. This is because training the generative neural network in thisgeneration scheme requires learning a distribution over a very largenumber of variables that preserves both global semantic coherence andexactness of detail.

This specification describes several generation schemes that account forthese and other issues and allow the image generation system to generatehigh quality images even when the image is large (e.g. at least 64pixels in each axis) while reducing how many computational resources areconsumed.

One generation technique that can be employed is referred to assubscaling, which is shown in illustration 104.

To perform subscaling, the system partitions the H by W pixel grid ofthe output image into K disjoint, interleaved sub-images (also known as“slices”) and orders the sub-images into a sub-image order. Because K isgreater than 1, each sub-image includes less than all of the pixels inthe image. The sub-images are referred to as being interleaved becausepixels within one sub-image are generally separated from other pixelswithin the same sub-image by pixels in another sub-image, i.e., pixelswithin a sub-image are not adjacent to each other within the outputimage.

In particular, to generate the partitioning, the system receives ascaling factor S and the system generates sub-images of size H/S×W/S byselecting a pixel every S pixels in both height and width, with eachsub-image having a different row and column offset relative to the othersub-images. This results in the entire spatial grid of the image beingcovered by K=S{circumflex over ( )}2 sub-images. For simplicity below itis assumed that H and W are multiples of S; if not, this can beaddressed in various ways, e.g. by padding the image with additionalpixels to increase H and W to be multiples of S.

The system then generates the sub-images one-by-one according to thesub-image order. Within each sub-image, the system generates intensityvalues autoregressively in raster-scan order of the pixels within thesub-image.

In the example shown in illustration 104, the system has divided the 4×4image into 4 2×2 sub-images and the sub-image order orders thesub-images in raster-scan order based on the locations of the top leftcorner pixel of each sub-image in the output image. Sub-image 1(according to the sub-image order) includes the pixels numbered 1, 2, 3,and 4 in illustration 104, sub-image 2 includes the pixels numbered 5,6, 7, 8, sub-image 3 includes the pixels numbered 9, 10, 11, and 12, andsub-image 4 includes the pixels numbered 13, 14, 15, and 16. As can beseen from illustration 104, the sub-images are interleaved, i.e., withpixel 1 assigned to sub-image 1 being separated from the other pixels insub-image 1 by pixels in the other sub-images.

The system then generates the intensity values within each sub-imageautoregressively, conditioned on intensity values for any pixels withinthe sub-image that have already been generated and intensity values forpixels in any sub-images that are before the sub-image in the sub-imageorder. That is, for each particular color channel for each particularpixel in each particular sub-image, the system, generates, using agenerative neural network, the intensity value for the particular colorchannel conditioned on intensity values for (i) any pixels that are insub-images that are before the particular sub-image in the ordering ofthe sub-images, (ii) any pixels within the particular sub-image that arebefore the particular pixel in a raster-scan order over the outputimage, and (iii) the particular pixel for any color channels that arebefore the particular color channel in the color channel order.Additionally, the intensity value for the particular color channel isnot conditioned on any intensity values that are for (i) any pixels thatare in sub-images that are after the particular sub-image in theordering of the sub-images, (ii) any pixels within the particularsub-image that are after the particular pixel in the raster-scan orderover the output image, and (iii) the particular pixel for any colorchannels that are after the particular color channel in the colorchannel order.

For example, as can be seen in illustration 104, pixel number 7, whichbelongs to sub-image 2, is the 7th pixel to be generated within theoutput image, after the 4 pixels in sub-image 1 and the 2 pixels insub-image 2 that are before pixel number 7 in raster-scan order over theoutput image. The intensity values for pixel number 7 will beconditioned on all of the intensity values for the pixels in sub-image1, the intensity values for pixels 5 and 6 in sub-image 2, and anyintensity values for any color channels of pixel number 7 that havealready been generated. The intensity values will not be conditioned onpixel number 8, which is in sub-image 2 but after pixel number 7 in theraster-scan order, or pixels 9-16, which are in sub-images 3 and 4 (thatare after sub-image 2 in the sub-image order).

As will be described in more detail below, subscaling allows the systemto more efficiently generate output images. In particular, subscalingallows the system to generate an output image by preserving, within thesub-images, the spatial structure of the pixels while compactlycapturing image-wide spatial dependencies when conditioning thegenerative neural network. Thus, the described systems require only afraction of the memory and the computation that would otherwise berequired to generate a large image while still generating high fidelityimages. In particular, when generating a particular sub-image, thisscheme can allow the system to condition a decoder neural network on adecoder input that has the same spatial dimensions as the sub-image andthat captures the image-wide spatial dependencies, no matter where inthe order the particular sub-image is located. Thus, the system cangenerate a large image while conditioning the decoder on decoder inputsthat have spatial dimensions that are much smaller than the spatialdimensions of the large image, i.e., that only have the same (muchsmaller) spatial dimensions as each of the sub-images of the largeimage.

Subscaling also allows the system to perform image upscaling, where alow-resolution image (such as an image of the real world, e.g. capturedby a camera) is transformed to a higher-resolution image of the samescene. In the example shown in FIG. 1, the system can perform up-scalingfrom a 2×2 image to a 16×16 image. In particular, illustration 106 showsthe system performing image up-scaling by using the input,lower-resolution image as the first sub-image in the sub-image order.That is, instead of generating the first sub-image, the system can fixthe first sub-image to be the input image and generate the remainingsub-images conditioned on the fixed first sub-image.

In the example shown in illustration 106, the system has received aninput 2×2 image and assigned the pixels of the input 2×2 image to be thepixels in the first sub-image, i.e., the pixels 1, 2, 3, and 4. Thesystem then generates the remaining pixels 5-16 as described above,conditioned on the fixed first sub-image. The pixels 5-16 are shaded inthe illustration 106 while pixels 1-4 are not because the shaded pixelsare generated by the system while the unshaded pixels are pixels thatare fixed based on the input image received by the system.

Instead of or in addition to subscaling, the system can also use a depthupscaling technique. In particular, the intensity value for any givenpixel in the output image can be represented as N bits, i.e., theintensity values are N-bit values.

To generate the output image when using depth upscaling, the systemfirst generates an initial H by W image, where the pixels in the initialH by W image include only the first b most significant bits of the N-bitintensity values for each of the color channels. The system can eithergenerate this initial image using subscaling or using the conventionalordering described above. The system then generates, from the initial Hby W image, the N−b least significant bits of the N-bit intensity valuesof the color channels for each of the pixels in the output image. Thatis, the system first generates the b most significant bits of each ofthe intensity values in the image and then generates the N−b leastsignificant bits of each of the intensity values in the imageconditioned at least on the most significant bits. The system can eithergenerate these additional bits using subscaling or using theconventional ordering described above.

Illustration 108 shows a combination of subscaling and depth upscaling.In the illustration 108, each pixel in the output image is divided intoan initial pixel (with b bit color intensity values) and an additionalpixel (with N−b color intensity values). Together, the initial pixel andthe additional pixel determine the N-bit intensity values for the outputpixel, i.e., by using the b bits of the initial pixel as the mostsignificant bits and the N−b bits as the least significant bits.

As shown in illustration 108, the system generates the initial pixels1-16 using the subscaling techniques described above. The system thengenerates the additional pixels 17-32 using the subscaling techniquesdescribed above, but also conditioned on the initial pixels 1-16. Thus,the system first generates an initial image that has b bit intensityvalues and then generates the remaining N−b bits of the Nbit intensityvalues in the final output image.

The combination of subscaling and depth subscaling can also allow thesystem to upscale the depth of an input low-resolution image while alsoup-scaling the resolution of the image. In the example shown inillustration 110, the system has received an input 2×2 image where allof the intensity values are b bit values. The system has assigned thepixels of the input 2×2 image to be the pixels in the first sub-image ofinitial pixels, i.e., the initial pixels 1, 2, 3, and 4, of the initialoutput image. The system then generates the remaining initial pixels5-16 of the initial output image as described above, conditioned on thefixed first sub-image, and then generates the least significant bits,i.e., the additional pixels 17-32, conditioned on the initial outputimage. The pixels 5-32 are shaded in the illustration 110 while pixels1-4 are not because the shaded pixels are generated by the system whilethe unshaded pixels are pixels that are fixed based on the input imagereceived by the system.

FIG. 2 shows an example image generation system 200 that performssubscale image generation. The image generation system 200 is an exampleof a system implemented as computer programs on one or more computers inone or more locations in which the systems, components, and techniquesdescribed below are implemented.

The system 200 generates a target sub-image 222 in the output imageconditioned on the sub-images that are before the target sub-image inthe sub-image order. In particular, the system 200 generates theintensity values in the target sub-image 222 conditioned on theintensity values for the pixels in any sub-images that are before thetarget sub-image in the sub-image order.

The system 200 includes an embedding neural network 210 and a decoderneural network 220.

To generate the target sub-image 220, the system 200 processes anembedding input 202 using the embedding neural network 210 to generatean encoded sub-image tensor.

The system 200 then auto-regressively generates the intensity values ofthe pixels in the target sub-image 222 conditioned on the encodedsub-image tensor generated by the embedding neural network 210 using thedecoder neural network 220. The generation is referred to asauto-regressive because the system 200 generates the intensity valueswithin the sub-image one-by-one, with the operations performed togenerate any particular intensity value being dependent on thealready-generated intensity values.

In particular, for each particular color channel for each particularpixel in the target sub-image 222, the system 200 generates, using thedecoder neural network 220, the intensity value for the particular colorchannel conditioned on (i) the encoded sub-image tensor that encodes theintensity values for pixels that are in sub-images that are before thetarget sub-image in the ordering of the sub-images, (ii) intensityvalues for any pixels within the target sub-image 222 that are beforethe particular pixel in a raster-scan order over the output image, and(iii) intensity values for the particular pixel for any color channelsthat are before the particular color channel in the color channel order.

As described above, the embedding input 202 to the embedding neuralnetwork 210 generally includes the intensity values for the sub-imagesthat are before the target sub-image 222 in the sub-image order. In theparticular example of FIG. 2, the target sub-image 222 is the sub-imagewith offset (n,m) in the output image relative to the top left of theoutput image. Thus, if the location of the top left pixel in theoriginal image is denoted by (0,0), the top left pixel in the targetsub-image 222 is the pixel at location (n,m) in the output image, thenext pixel in raster-scan order is the pixel at location (n,m+S), andthe last pixel in the sub-image in raster-scan order is the pixel atlocation (n+H−S,m+W−S) in the output image.

Accordingly, the embedding input 202 includes the intensity values forthe sub-images ahead of the target sub-image 222 in the sub-image order,i.e., the sub-images with offsets less that are before pixel (n,m) inraster-scan order of the output image, i.e., the sub-images with offsetsthat have row offsets of less than n and sub-images with offsets equalto n but column offsets less than m.

As a particular example, the embedding input 202 can include the alreadygenerated sub-images concatenated along the depth dimension. In some ofthese cases, the embedding input 202 can include empty paddingsub-images, i.e., sub-images with all intensity values set to zero or toanother predetermined default value, to preserve the ordering of eachalready generated sub-image relative to the target sub-image and toensure that the embedding input 202 is the same size for each sub-image,i.e., so that the total number of sub-images in the depth concatenatedinput is always the same.

In FIG. 2, this scheme for generating the embedding input 202 isillustrated as follows: sub-images are represented by rectangles, andthe rectangles within the dashed lines are depth concatenated inraster-scan order to generate the embedding input 202 for the targetsub-image 222. Additionally, the rectangles within the solid lines arethe sub-images that are part of the output image, while the rectanglesinside the dashed lines but outside the solid lines are the emptypadding sub-images that are added to the embedding input 202 to fix thesize of the input and preserve relative positions within the embeddinginput 202. The rectangles outside the dashed lines but within the solidlines, on the other hand, are the sub-images that are after the targetsub-image 222 in the sub-image generation order and are therefore notincluded in the embedding input 202.

In some cases, the embedding input 202 can also include data specifyinga position of the particular sub-image in the ordering. For example, theembedding input 202 can include the meta-position of the targetsub-image, i.e., the offset coordinates of the target sub-image, as anembedding of 8 units tiled spatially across a sub-image tensor.

The system can represent intensity values in any of a variety of ways ininputs that are processed by the embedding neural network 210 and thedecoder 220. For example, the system can represent intensity values asfloating point numbers. As another example, the system can representintensity values as binary vectors. As another example, the system canrepresent intensity values as one-hot encoded vectors. As yet anotherexample, the system can represent intensity values as either pre-trainedor jointly learned embeddings having a fixed dimensionality, e.g., aneight dimensional vector or a sixteen dimensional vector.

The embedding neural network 210 can have any appropriate structure thatallows the neural network to process the embedding input 202 to generatean encoded sub-image tensor that summarizes the context of the targetsub-image 222 for use by the decoder neural network 220.

The encoded sub-image tensor is generally a feature map has the samespatial size as the sub-images of the output image, i.e., H/S×W/S. Thatis, the encoded sub-image tensor includes a respective encodedrepresentation, i.e., a respective feature vector, for each position inthe target sub-image 222.

As a particular example, the embedding neural network 210 can be aconvolutional neural network with residual blocks. A residual blockrefers to a sequence of layers, including one or more convolutionallayers, that have an input connection between the input to the firstlayer of the block and the output of the last layer in the block. Insome cases, the embedding neural network 210 includes a series ofself-attention layers that are followed by multiple residual blocks ofconvolutional layers.

The decoder neural network 220 receives the encoded sub-image tensor anduses the encoded sub-image tensor to autoregressively generate theintensity values for the pixels in the target sub-image 222 inraster-scan order.

In particular, the decoder neural network 220 takes as input the encodedsub-image tensor in a position-preserving manner, i.e., so that theassociations between encoded representations and their correspondingpositions in the target sub-image 222 are preserved. That is, theencoded sub-image tensor is spatially aligned with the tensor thatincludes the intensity values of the target sub-image, so that theencoded representation of a given intensity value from previoussub-images is located at the same spatial location as the correspondingintensity value in the target sub-image. This can be accomplished by, ateach iteration during the auto-regressive generation, depthconcatenating a representation of the current target sub-image as of theiteration with the encoded sub-image tensor as will be described below.

The decoder neural network 220 can generally have any architecture thatallows the decoder to receive as input, for a given pixel within thesub-image and a given color channel (i) the encoded sub-image tensor and(ii) the already generated intensity values for pixels within thesub-image and to generate an output that defines a probabilitydistribution over possible intensity values for the given color channelof the given pixel. The system 200 can then select the intensity valuefor the given color based on the probability distribution, e.g., bysampling a value from the distribution or selecting the value with thehighest probability.

As a particular example, the decoder neural network 220 can have ahybrid architecture that combines masked convolution and self-attentionto generate intensity values conditioned only on already generatedintensity values within the sub-image and the encoded sub-image tensor.For example, the system can reshape the sub-image into a one-dimensionaltensor and then apply a one-dimensional masked self-attention neuralnetwork that attends over the already generated intensity values (whilenot attending to any future intensity values due to the masking) togenerate an attended one-dimensional tensor. The system can then reshapethe attended one-dimensional tensor into a two-dimensional tensor anddepth concatenate the two-dimensional tensor with the encoded sub-imagetensor and provide the depth concatenated tensor as a conditioning inputto a gated convolutional neural network that applies masked convolutionsto generate the distribution over intensity values. An example onedimensional masked self-attention neural network is described inAttention is All you Need, Vaswani, et al, arXiv:1706.03762. An examplegated convolutional neural network is described in Conditional ImageGeneration with PixelCNN Decoders, van den Oord, et al,arXiv:1606.05328.

During training, this can be performed in parallel for all of the pixelsin the sub-image, while after training and during inference, the decoderneural network 220 processes auto-regressively to generate intensityvalues within the sub-image one by one in raster-scan order.

As can be seen in the above description, the system can generate alarge, high-fidelity image even though the spatial dimensions of thetensors processed by the embedding neural network and the decoder neuralnetwork are fixed to the dimensions of the slices of the larger outputimage. For example, using 32×32 slices, the system can generate a128×128 or 256×256 output image while only needing to process tensorsthat have dimensions 32×32. This allows the system to preserve in thesub-images the spatial structure of the pixels while compactly capturingimage-wide spatial dependencies even when the size of the output imageto be generated is quite large.

In particular, as can be seen above, the embedding neural network 210and the decoder neural network 220 jointly generate an H×W image whileonly processing inputs that have smaller spatial dimensions, i.e., theH/S×W/S dimensions of the sub-images. Thus, this scheme can allow thesystem to condition the decoder neural network 210 in a manner thatcaptures the image-wide spatial dependencies without needing to processtensors with large spatial dimensionalities no matter where in the orderthe particular sub-image is located. Thus, the system can generate alarge image while conditioning the embedding network and the decoder oninputs that have spatial dimensions that are much smaller than thespatial dimensions of the large image, i.e., that only have the same(much smaller) spatial dimensions as each of the sub-images of the largeimage. This can result in a significant savings in memory and processingpower relative to conditioning a generative neural network on all of thepreviously generated intensity values directly while still effectivelycapturing image-wide dependencies.

In some cases, the system 200 generates the output image conditioned ona conditioning input 204.

In some of these cases, the system performs super-resolution to generatehigher resolution versions of input images. That is, the conditioninginput 204 is a lower-resolution image. In these cases, the system 200can generate the first sub-image in the sub-image order from thelower-resolution image as described above and then proceed withgenerating the remainder of the sub-images in the output image. In otherwords, the first sub-image is fixed to the lower-resolution imageinstead of generated by the system 200.

In others of these cases, the system 200 receives a differentconditioning input 204 that identifies properties of an image andgenerates an output image that has the identified properties. In otherwords, the conditioning input 204 is a conditioning tensorcharacterizing a desired content of the output image, e.g., a desiredcategory label for the output image. In these cases, the system 200 cancondition the activation functions of the convolutional layers in theembedding neural network 210, the decoder neural network 220, or both onthe conditioning tensor. Conditioning activation functions ofconvolutional layers on a conditioning tensor is described in moredetail in Conditional Image Generation with PixelCNN Decoders, van denOord, et al, arXiv:1606.05328.

The system can train the embedding neural network 210 and the decoderneural network 220 jointly to cause the embedding neural network 210 andthe decoder neural network 220 to generate high quality output images.

In particular, the system 200 can train these neural networks byrepeatedly obtaining ground truth images, i.e., output images thatshould be generated by the system and, when used, conditioning inputsfor the ground truth images. The system 200 can then uniformly sample asub-image from each ground truth image and generate the sampledsub-image using the neural networks conditioned on the earliersub-images from the ground truth image (and the conditioning input, whenused). The system 200 can then determine gradients of a loss thatmeasures the log likelihood of the intensity values in the ground truthimage according to the probability distributions generated by the neuralnetworks when generating the sampled sub-image and update the values ofthe parameters of the neural networks using the determined gradientsusing an appropriate neural network optimizer, e.g., rmsProp, Adam, orstochastic gradient descent. By repeatedly performing this updating, thesystem 200 generates trained parameter values that result in highfidelity images being generated. Because the system 200 only needs togenerate a relatively small sized sub-image for each ground truth outputimage (rather than the entire output image) in order to update theparameters of the networks, the system 200 can perform this training ina computationally efficient manner.

FIG. 3 shows an image generation system 300 that generates output imagesusing depth upscaling.

In particular, the system 300 generates H by W output images that haveN-bit intensity values using depth upscaling by first generating aninitial H by W output image 312 that includes b bit intensity values andthen generating an additional H by W output image 322 that has H-b bitintensity values. Generally, b is an integer that is less than N. Forexample, when N is eight, i.e., the output image is an image with 8 bitintensity values, b can be three or four. As another example, when N issixteen, b can be three or six.

The system 300 can then generate a final output image 324 that includesN-bit intensity values by, for each intensity value, using the b bits ofthe corresponding intensity value, i.e., the intensity value for thesame color channel of the same pixel, in the initial output image 312 asthe b most significant bits of the N bits and the N-b bits of thecorresponding intensity value in the additional output image 322 as theN-b least significant bits of the N bits.

More specifically, the system 300 includes a first generative neuralnetwork 310 and a second generative neural network 320.

The first generative neural network 310 is configured to generate theinitial output image 312, optionally conditioned on a conditioning input302.

The second generative neural network 320 is configured to generate theadditional output image 322 conditioned on the initial output image 312and optionally also conditioned on the conditioning input 302.

For example, when the second generative neural network 320 includes anembedding neural network and a decoder neural network as described abovewith FIG. 2, the second generative neural network 320 can be conditionedon the initial output image 312 by modifying the embedding inputs thatare generated for each sub-image of the additional output image 312. Inparticular, the system 300 can divide the initial output image 312 intosub-images, i.e., using the subscale technique described above, and thenadd the sub-images to the embedding input, e.g., by depth concatenatingthe sub-images with the padding sub-images and the already generatedsub-images.

In some cases, the conditioning input 302 is a lower bit-depth image.That is, the conditioning input is an H by W image with b-bit intensityvalues. In these cases, the system 300 can depth upscale theconditioning image to an image that has N-bit intensity values, i.e., toa higher quality output image. To do so, the system bypasses the firstneural network 310 and uses the conditioning image as the initial outputimage 312, i.e., only performs the processing of the second neuralnetwork 320 conditioned on the conditioning image, and then generatesthe final output image 324 from the conditioning image and theadditional image 322.

In other cases, e.g., when the conditioning input is a lower-resolutionimage or a conditioning tensor, the conditioning input 302 can conditionthe generation of the output image on the conditioning input 302 asdescribed above with reference to FIG. 2.

Generating output images using depth upscaling is described in moredetail below with reference to FIG. 5.

FIG. 4 is a flow diagram of an example process 400 for generating anoutput image using sub scaling. For convenience, the process 400 will bedescribed as being performed by a system of one or more computerslocated in one or more locations. For example, an image generationsystem, e.g., the image generation system 200 of FIG. 2, appropriatelyprogrammed, can perform the process 400.

In the example of FIG. 4, the output image being generated has aplurality of pixels arranged in an H by W pixel grid and each pixelincludes a respective intensity value for each of one or more colorchannels that are ordered according to a color channel order. Thus, inorder to generate the output image, the system needs to generate each ofthe intensity values for each of the pixels in the output image.

The system obtains data specifying (i) a partitioning of the H by Wpixel grid into K disjoint, interleaved sub-images, wherein K is aninteger that is less H, and (ii) an ordering of the sub-images (step402). In some implementations, the system receives a scaling factor andgenerates the K sub-images based on the scaling factor as describedabove. In some other implementations, the system receives dataidentifying which pixels in the image are in which sub-image.

The system then generates intensity values sub-image by sub-imageaccording to the ordering of the sub-images. In particular, for eachparticular color channel for each particular pixel in each particularsub-image, the system generates, using a generative neural network, theintensity value for the particular color channel conditioned onintensity values for (i) any pixels that are in sub-images that arebefore the particular sub-image in the ordering of the sub-images, (ii)any pixels within the particular sub-image that are before theparticular pixel in a raster-scan order over the output image, and (iii)the particular pixel for any color channels that are before theparticular color channel in the color channel order.

In some implementations the generative neural network includes theembedding neural network and the decoder neural network of FIG. 2 andthe system generates the output image by performing steps 404 and 406for each sub-image, starting from the first sub-image in the sub-imageorder and continuing in accordance with the sub-image order until thelast sub-image in the order.

The system generates an encoded sub-image tensor for the sub-image fromintensity values already generated for pixels in sub-images before thesub-image in the generation order using the embedding neural network(step 404).

The system autoregressively generates the intensity values for thepixels in the sub-image using the decoder neural network (step 406).Each intensity value is generated conditioned on the encoded sub-imagetensor and on the intensity values that have already been generated forpixels in the sub-image.

FIG. 5 is a flow diagram of an example process 500 for generating anoutput image using depth upscaling. For convenience, the process 500will be described as being performed by a system of one or morecomputers located in one or more locations. For example, an imagegeneration system, e.g., the image generation system 200 of FIG. 2,appropriately programmed, can perform the process 500.

In the example of FIG. 5, the output image being generated has aplurality of pixels arranged in an H by W pixel grid and each pixelincludes a respective intensity value for each of one or more colorchannels that are ordered according to a color channel order. Eachintensity value is an N-bit value. Thus, in order to generate the outputimage, the system needs to generate the N bits for each of the intensityvalues for each of the pixels in the output image.

The system generates, using a first generative neural network, aninitial H by W image (step 502). The intensity values for the pixels inthe initial H by W image include only the first b most significant bitsof the N bit intensity values for each of the color channels. Because bis less than N, the intensity values include only a proper subset of theintensity values that are required to be generated for the output image.The system can generate this initial output image using the generativeneural network described above with reference to FIGS. 1, 2, and 4,i.e., a generative neural network that includes an embedding neuralnetwork and a decoder neural network that generates images usingsubscaling. Alternatively, the system can generate this initial outputimage using a generative neural network that uses the conventionalordering scheme described above in the illustration 102. Some examplesof recurrent generative neural networks and convolutional generativeneural networks that can generate images in this manner are described inPixelRNN, van den Oord, et al, arXiv:1601.06759. Other examples ofconvolutional generative neural networks are described in ConditionalImage Generation with PixelCNN Decoders, van den Oord, et al,arXiv:1606.05328.

The system generates, from the initial H by W image and using a secondgenerative neural network, the N−b least significant bits of the N bitintensity values of the color channels for each of the pixels in theoutput image (step 504). That is, the second generative neural networkgenerates an H by W image that has N−b bit intensity values. The secondgenerative neural network generates the N−b least significant bits ofthe N bit intensity values conditioned on the initial output image,i.e., conditioned on the b most significant bits of each of theintensity values.

When the second generative neural network includes an embedding neuralnetwork and a decoder neural network as described above with FIG. 2, thesecond generative neural network can be conditioned on the initialoutput image by modifying the embedding inputs that are generated foreach sub-image of the additional output image. In particular, the systemcan divide the initial output image into sub-images, i.e., using thesubscale technique described above, and then add the sub-images to theembedding input, e.g., by depth concatenating the sub-images with thepadding sub-images and the already generated sub-images.

The system generates a final output image by, for each intensity valuein the image, using the b bits generated by the first generative neuralnetwork as the most significant bits of the intensity value and the N-bbits generated by the second neural network as the least significantbits of the intensity value (step 506).

As described above, in some cases the system combines depth upscalingand subscaling by generating the initial output image, the additionaloutput image, or both using subscaling.

Additionally, as described above, in some cases the conditioning inputis a lower-resolution, lower-bit depth image. In these cases, the systemcan generate the output image by generating the initial output imageusing subscaling and fixing the first sub-image of the initial outputimage to be the lower-resolution, lower-bit depth input image.

This specification uses the term “configured” in connection with systemsand computer program components. For a system of one or more computersto be configured to perform particular operations or actions means thatthe system has installed on it software, firmware, hardware, or acombination of them that in operation cause the system to perform theoperations or actions. For one or more computer programs to beconfigured to perform particular operations or actions means that theone or more programs include instructions that, when executed by dataprocessing apparatus, cause the apparatus to perform the operations oractions.

Embodiments of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly-embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Embodiments of the subject matter described in thisspecification can be implemented as one or more computer programs, i.e.,one or more modules of computer program instructions encoded on atangible non transitory storage medium for execution by, or to controlthe operation of, data processing apparatus. The computer storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them. Alternatively or in addition, the programinstructions can be encoded on an artificially generated propagatedsignal, e.g., a machine-generated electrical, optical, orelectromagnetic signal, that is generated to encode information fortransmission to suitable receiver apparatus for execution by a dataprocessing apparatus.

The term “data processing apparatus” refers to data processing hardwareand encompasses all kinds of apparatus, devices, and machines forprocessing data, including by way of example a programmable processor, acomputer, or multiple processors or computers. The apparatus can alsobe, or further include, special purpose logic circuitry, e.g., an FPGA(field programmable gate array) or an ASIC (application specificintegrated circuit). The apparatus can optionally include, in additionto hardware, code that creates an execution environment for computerprograms, e.g., code that constitutes processor firmware, a protocolstack, a database management system, an operating system, or acombination of one or more of them.

A computer program, which may also be referred to or described as aprogram, software, a software application, an app, a module, a softwaremodule, a script, or code, can be written in any form of programminglanguage, including compiled or interpreted languages, or declarative orprocedural languages; and it can be deployed in any form, including as astand alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A program may, but neednot, correspond to a file in a file system. A program can be stored in aportion of a file that holds other programs or data, e.g., one or morescripts stored in a markup language document, in a single file dedicatedto the program in question, or in multiple coordinated files, e.g.,files that store one or more modules, sub programs, or portions of code.A computer program can be deployed to be executed on one computer or onmultiple computers that are located at one site or distributed acrossmultiple sites and interconnected by a data communication network.

In this specification, the term “database” is used broadly to refer toany collection of data: the data does not need to be structured in anyparticular way, or structured at all, and it can be stored on storagedevices in one or more locations. Thus, for example, the index databasecan include multiple collections of data, each of which may be organizedand accessed differently.

Similarly, in this specification the term “engine” is used broadly torefer to a software-based system, subsystem, or process that isprogrammed to perform one or more specific functions. Generally, anengine will be implemented as one or more software modules orcomponents, installed on one or more computers in one or more locations.In some cases, one or more computers will be dedicated to a particularengine; in other cases, multiple engines can be installed and running onthe same computer or computers.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby special purpose logic circuitry, e.g., an FPGA or an ASIC, or by acombination of special purpose logic circuitry and one or moreprogrammed computers.

Computers suitable for the execution of a computer program can be basedon general or special purpose microprocessors or both, or any other kindof central processing unit. Generally, a central processing unit willreceive instructions and data from a read only memory or a random accessmemory or both. The essential elements of a computer are a centralprocessing unit for performing or executing instructions and one or morememory devices for storing instructions and data. The central processingunit and the memory can be supplemented by, or incorporated in, specialpurpose logic circuitry. Generally, a computer will also include, or beoperatively coupled to receive data from or transfer data to, or both,one or more mass storage devices for storing data, e.g., magnetic,magneto optical disks, or optical disks. However, a computer need nothave such devices. Moreover, a computer can be embedded in anotherdevice, e.g., a mobile telephone, a personal digital assistant (PDA), amobile audio or video player, a game console, a Global PositioningSystem (GPS) receiver, or a portable storage device, e.g., a universalserial bus (USB) flash drive, to name just a few.

Computer readable media suitable for storing computer programinstructions and data include all forms of non volatile memory, mediaand memory devices, including by way of example semiconductor memorydevices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks,e.g., internal hard disks or removable disks; magneto optical disks; andCD ROM and DVD-ROM disks.

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube) or LCD (liquidcrystal display) monitor, for displaying information to the user and akeyboard and a pointing device, e.g., a mouse or a trackball, by whichthe user can provide input to the computer. Other kinds of devices canbe used to provide for interaction with a user as well; for example,feedback provided to the user can be any form of sensory feedback, e.g.,visual feedback, auditory feedback, or tactile feedback; and input fromthe user can be received in any form, including acoustic, speech, ortactile input. In addition, a computer can interact with a user bysending documents to and receiving documents from a device that is usedby the user; for example, by sending web pages to a web browser on auser's device in response to requests received from the web browser.Also, a computer can interact with a user by sending text messages orother forms of message to a personal device, e.g., a smartphone that isrunning a messaging application, and receiving responsive messages fromthe user in return.

Data processing apparatus for implementing machine learning models canalso include, for example, special-purpose hardware accelerator unitsfor processing common and compute-intensive parts of machine learningtraining or production, i.e., inference, workloads.

Machine learning models can be implemented and deployed using a machinelearning framework, e.g., a TensorFlow framework, a Microsoft CognitiveToolkit framework, an Apache Singa framework, or an Apache MXNetframework.

Embodiments of the subject matter described in this specification can beimplemented in a computing system that includes a back end component,e.g., as a data server, or that includes a middleware component, e.g.,an application server, or that includes a front end component, e.g., aclient computer having a graphical user interface, a web browser, or anapp through which a user can interact with an implementation of thesubject matter described in this specification, or any combination ofone or more such back end, middleware, or front end components. Thecomponents of the system can be interconnected by any form or medium ofdigital data communication, e.g., a communication network. Examples ofcommunication networks include a local area network (LAN) and a widearea network (WAN), e.g., the Internet.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other. In someembodiments, a server transmits data, e.g., an HTML page, to a userdevice, e.g., for purposes of displaying data to and receiving userinput from a user interacting with the device, which acts as a client.Data generated at the user device, e.g., a result of the userinteraction, can be received at the server from the device.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or on the scope of what may be claimed, but rather asdescriptions of features that may be specific to particular embodimentsof particular inventions. Certain features that are described in thisspecification in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable subcombination. Moreover, although features may be describedabove as acting in certain combinations and even initially be claimed assuch, one or more features from a claimed combination can in some casesbe excised from the combination, and the claimed combination may bedirected to a subcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings and recited inthe claims in a particular order, this should not be understood asrequiring that such operations be performed in the particular ordershown or in sequential order, or that all illustrated operations beperformed, to achieve desirable results. In certain circumstances,multitasking and parallel processing may be advantageous. Moreover, theseparation of various system modules and components in the embodimentsdescribed above should not be understood as requiring such separation inall embodiments, and it should be understood that the described programcomponents and systems can generally be integrated together in a singlesoftware product or packaged into multiple software products.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In some cases, multitasking and parallel processing may beadvantageous.

What is claimed is:
 1. A method of generating an output image having aplurality of pixels arranged in an H by W pixel grid, wherein each pixelincludes a respective intensity value for each of one or more colorchannels that are ordered according to a color channel order, andwherein the method comprises: obtaining data specifying (i) apartitioning of the H by W pixel grid into K disjoint, interleavedsub-images, wherein K is an integer that is less H, and (ii) an orderingof the sub-images; and generating intensity values sub-image bysub-image according to the ordering of the sub-images, comprising: foreach particular color channel for each particular pixel in eachparticular sub-image, generating, using a generative neural network, theintensity value for the particular color channel conditioned onintensity values for (i) any pixels that are in sub-images that arebefore the particular sub-image in the ordering of the sub-images, (ii)any pixels within the particular sub-image that are before theparticular pixel in a raster-scan order over the output image, and (iii)the particular pixel for any color channels that are before theparticular color channel in the color channel order, wherein for eachparticular color channel for each particular pixel in each particularsub-image, the intensity value for the particular color channel is notconditioned on any intensity values that are for (i) any pixels that arein sub-images that are after the particular sub-image in the ordering ofthe sub-images, (ii) any pixels within the particular sub-image that areafter the particular pixel in the raster-scan order over the outputimage, and (iii) the particular pixel for any color channels that areafter the particular color channel in the color channel order.
 2. Themethod of claim 1 wherein the ordering of the sub-images orders thesub-images in raster-scan order based on the locations of the top leftcorner pixel of each sub-image in the output image.
 3. The method ofclaim 1, wherein generating the intensity values comprises, for eachparticular sub-image: processing an embedding input comprising intensityvalues already generated for sub-images before the particular sub-imagein the ordering using an embedding neural network to generate an encodedsub-image tensor; and auto-regressively generating the intensity valuesof the pixels in the particular sub-image conditioned on the encodedsub-image tensor using a decoder neural network.
 4. The method of claim3, wherein the embedding input comprises the already generatedsub-images concatenated along a depth dimension.
 5. The method of claim4, wherein the embedding input comprises empty padding sub-images topreserve the ordering of each already generated sub-image relative tothe particular sub-image.
 6. The method of claim 3, wherein theembedding input comprises data specifying a position of the particularsub-image in the ordering.
 7. The method of claim 3, wherein theembedding neural network is a convolutional neural network with residualblocks.
 8. The method of claim 3 wherein the decoder neural networkgenerates the intensity values of the pixels in the particular sub-imagein raster-scan order within the particular sub-image.
 9. The method ofclaim 3, wherein the decoder neural network takes as input the encodedsub-image tensor in a position-preserving manner.
 10. The method ofclaim 3, wherein the decoder neural network processes a decoder inputthat comprises the encoded sub-image tensor and that has a same spatialdimensionality as the sub-images.
 11. The method of claim 3, wherein thedecoder neural network has a hybrid architecture that combines maskedconvolution and self-attention.
 12. The method of claim 3 furthercomprising obtaining a conditioning input and wherein generatingintensity values comprises conditioning each intensity value on theconditioning input.
 13. The method of claim 12, wherein the conditioninginput comprises a lower-resolution image, and wherein generatingintensity values comprises setting the lower-resolution image to be thefirst sub-image in the ordering.
 14. The method of claim 12, wherein theconditioning input comprises a low bit-depth H by W image.
 15. Themethod of claim 14 when dependent on any one of claims 4-12, whereingenerating the intensity values comprises including sub-images from thelow bit-depth H by W image in the embedding input for the encoder neuralnetwork.
 16. The method of claim 12, wherein the conditioning input is aconditioning tensor characterizing a desired content of the outputimage, wherein the generative neural network comprises one or moreconvolutional layers, and wherein generating the intensity valuescomprises conditioning an activation function of the convolutionallayers on the conditioning tensor.
 17. The method of claim 1 furthercomprising obtaining a conditioning input and wherein generatingintensity values comprises conditioning each intensity value on theconditioning input.
 18. One or more non-transitory computer-readablestorage media storing instructions that when executed by one or morecomputers cause the one or more computers to perform operations forgenerating an output image having a plurality of pixels arranged in an Hby W pixel grid, wherein each pixel includes a respective intensityvalue for each of one or more color channels that are ordered accordingto a color channel order, the operations comprising: obtaining dataspecifying (i) a partitioning of the H by W pixel grid into K disjoint,interleaved sub-images, wherein K is an integer that is less H, and (ii)an ordering of the sub-images; and generating intensity values sub-imageby sub-image according to the ordering of the sub-images, comprising:for each particular color channel for each particular pixel in eachparticular sub-image, generating, using a generative neural network, theintensity value for the particular color channel conditioned onintensity values for (i) any pixels that are in sub-images that arebefore the particular sub-image in the ordering of the sub-images, (ii)any pixels within the particular sub-image that are before theparticular pixel in a raster-scan order over the output image, and (iii)the particular pixel for any color channels that are before theparticular color channel in the color channel order, wherein for eachparticular color channel for each particular pixel in each particularsub-image, the intensity value for the particular color channel is notconditioned on any intensity values that are for (i) any pixels that arein sub-images that are after the particular sub-image in the ordering ofthe sub-images, (ii) any pixels within the particular sub-image that areafter the particular pixel in the raster-scan order over the outputimage, and (iii) the particular pixel for any color channels that areafter the particular color channel in the color channel order.
 19. Thenon-transitory computer-readable storage media of claim 18 theoperations further comprising obtaining a conditioning input and whereingenerating intensity values comprises conditioning each intensity valueon the conditioning input.
 20. The non-transitory computer-readablestorage media of claim 18, wherein generating the intensity valuescomprises, for each particular sub-image: processing an embedding inputcomprising intensity values already generated for sub-images before theparticular sub-image in the ordering using an embedding neural networkto generate an encoded sub-image tensor; and auto-regressivelygenerating the intensity values of the pixels in the particularsub-image conditioned on the encoded sub-image tensor using a decoderneural network.
 21. The non-transitory computer-readable storage mediaof claim 20 wherein the decoder neural network generates the intensityvalues of the pixels in the particular sub-image in raster-scan orderwithin the particular sub-image.
 22. The non-transitorycomputer-readable storage media of claim 20, wherein the decoder neuralnetwork takes as input the encoded sub-image tensor in aposition-preserving manner.
 23. The non-transitory computer-readablestorage media of claim 20, wherein the decoder neural network processesa decoder input that comprises the encoded sub-image tensor and that hasa same spatial dimensionality as the sub-images.
 24. A system comprisingone or more computers and one or more storage devices storinginstructions that when executed by one or more computers cause the oneor more computers to perform operations for generating an output imagehaving a plurality of pixels arranged in an H by W pixel grid, whereineach pixel includes a respective intensity value for each of one or morecolor channels that are ordered according to a color channel order, theoperations comprising: obtaining data specifying (i) a partitioning ofthe H by W pixel grid into K disjoint, interleaved sub-images, wherein Kis an integer that is less H, and (ii) an ordering of the sub-images;and generating intensity values sub-image by sub-image according to theordering of the sub-images, comprising: for each particular colorchannel for each particular pixel in each particular sub-image,generating, using a generative neural network, the intensity value forthe particular color channel conditioned on intensity values for (i) anypixels that are in sub-images that are before the particular sub-imagein the ordering of the sub-images, (ii) any pixels within the particularsub-image that are before the particular pixel in a raster-scan orderover the output image, and (iii) the particular pixel for any colorchannels that are before the particular color channel in the colorchannel order, wherein for each particular color channel for eachparticular pixel in each particular sub-image, the intensity value forthe particular color channel is not conditioned on any intensity valuesthat are for (i) any pixels that are in sub-images that are after theparticular sub-image in the ordering of the sub-images, (ii) any pixelswithin the particular sub-image that are after the particular pixel inthe raster-scan order over the output image, and (iii) the particularpixel for any color channels that are after the particular color channelin the color channel order.
 25. The system of claim 24 the operationsfurther comprising obtaining a conditioning input and wherein generatingintensity values comprises conditioning each intensity value on theconditioning input.
 26. The system of claim 24, wherein generating theintensity values comprises, for each particular sub-image: processing anembedding input comprising intensity values already generated forsub-images before the particular sub-image in the ordering using anembedding neural network to generate an encoded sub-image tensor; andauto-regressively generating the intensity values of the pixels in theparticular sub-image conditioned on the encoded sub-image tensor using adecoder neural network.
 27. The system of claim 26 wherein the decoderneural network generates the intensity values of the pixels in theparticular sub-image in raster-scan order within the particularsub-image.
 28. The system of claim 26, wherein the decoder neuralnetwork takes as input the encoded sub-image tensor in aposition-preserving manner.
 29. The system of claim 26, wherein thedecoder neural network processes a decoder input that comprises theencoded sub-image tensor and that has a same spatial dimensionality asthe sub-images.